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## AAMP Training Materials

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**AAMP Training Materials**Nicholas Minot (IFPRI) n.minot@cgiar.org Module 3.2: Measuring Food Price Transmission**Objectives**• Understand what price transmission is and why it occurs • Compute elasticity of price transmission • Measure price transmission • Simple percentage changes • Correlation analysis • Regression analysis • Examine non-stationary data**Background Material**• What is price transmission? • Why is it important to study price transmission? • Why does price transmission occur? • Introduction to elasticity of price transmission**What is price transmission?**• Price transmission is when a change in one price causes another price to change • Three types of price transmission: • Spatial: Price of maize in South Africa price of maize in Mozambique • Vertical: Price of wheat price of flour • Cross-commodity: Price of maize price of rice**Why is it important to study price transmission?**• Study of price transmission helps to understand causes of changes in prices, necessary to address root causes • Example: If little price transmission from world markets, then trade policy will not be effective in reducing volatility • Study of price transmission may help forecast prices based on trends in related prices • Example: If changes in soybean prices transmitted to sunflower markets, then soybean futures markets may predict sunflower prices • Study of price transmission helps diagnose poorly functioning markets • Example: If two markets are close together, but show little price transmission, this may indicate problems with transportation network or monopolistic practices**Why does price transmission occur?**• Spatial price transmission occurs because of flows of goods between markets • If price gap > marketing costs, trade flows will narrow gap • If price gap < marketing cost, no flows • Therefore, price gap <= marketing cost Maize prices in Maputo & Chokwe**Why does price transmission occur?**• Vertical price transmission occurs because of flows of goods along marketing channel Maize grain and maize meal prices in Kitwe, Zambia Maize meal Maize grain**Why does price transmission occur?**• Cross-commodity price transmission occurs because of substitution in consumption and/or production Price of maize and rice in Maputo**Why might price transmission not occur?**• High transportation cost makes trade unprofitable • Trade barriers make trade unprofitable • Goods are imperfect substitutes (e.g. imported rice and local rice) • Lack of information about prices in other markets • Long time to transport from one market to another (lagged transmission)**What is an elasticity of price transmission?**• Price transmission elasticity: % change in one price for each 1% increase in the other price • Example: if a 10% increase in the world price of maize causes a 3% increase in the local price of maize, then price transmission elasticity is: 0.03 / 0.10 = 0.3**What is an elasticity of price transmission?**• Elasticity of 1.0 is not always “perfect transmission” • Example: • World price = $200/ton • Local price = $400/ton • Perfect transmission would be if a $100 increase in world price caused a $100 increase in local price • But transmission elasticity in this case would be (100/400)/(100/200)= .25 / .50 = 0.50 • For imports, perfect transmission elasticity are < 1.0 • For exports, perfect transmission elasticity are > 1.0**Measuring price transmission**• There are several methods – four are discussed here • Ratio of percentage changes between two time periods • Correlation coefficient • Regression analysis • Co-integration analysis**Ratio of percentages**Ratio of percentage changes between two time periods Elasticity of transmission is 1.34 (= .99 / .74) Note that both prices increased by about $120/ton**Ratio of percentages**• Very crude method: only uses two points in time and does not take trends into account**Correlation coefficient – What is it?**• Indicates the degree of relatedness of two variables • Two related measures • Pearson correlation coefficient = r • Coefficient of determination = R2 = r * r • In both cases • Correlation ranges between 0 and 1 • 0 means no relationship, 1 means perfect correlation • Advantage: • Easy to calculate and understand • R2 indicates share of variation in one variable explained by other variable • Disadvantage: • Only considers relationship between prices at same time, does not take into account lags**Correlation coefficient – How to calculate?**Two methods using Excel • Use function correl(range1, range2) where the range1 and range2 describe the cells containing the two variables • For example, type into a cell =correl(B4:B56, C4:C56) • This will give r, R2 can be calculated by squaring r • Create scatterplot graph of the two variables, then add a trendline with R2 • Click on graph, click “Add trendline”, then click “Display R2” • This will give R2**Examples of correlation coefficients(hypothetical prices)**Weak correlation Strong correlation Medium correlation**Correlation coefficient – Exercises**• In Worksheet 1 [Tanzania example], type =CORREL(B5:B51,C5:C51) into cell F21 to calculate r • Then in F22 cell, type =F21*F21 (or = F21^2) to calculate R2 • In Worsheet 8 [Data], calculate the value of R2 for the following pairs of prices: • Maize in Nampula and rice in Nampula • Rice in Nampula and rice in Maputo • Maize in Nampula and rice in Maputo**Regression analysis**• Multiple regression analysis finds the equation that best fits the data: Y = a + b*X1 + c*X2 … • Advantages • Gives information to calculate transmission elasticity • Can test relationships statistically • Can take into account lagged effects, inflation, and seasonality • can analyze relationship of > 2 prices • Disadvantages • Awkward to do in Excel (easier with Stata or SPSS) • Misleading results if data are non-stationary**Regression analysis**Method 1: The Scatter Graph Using Excel 2003 • Mark columns with 2 prices • Insert/Chart/XY (Scatter) / Finish • Chart/Add trendline/ Linear • Click “Options”, then “Display equation” Using Excel 2007 • Mark columns with 2 prices • Insert/Scatter graph • Chart tools/Layout/Trendline/More • Click box for “Display equation on chart” Note: only one “x” allowed with this method**Regression analysis**Method 1: The Scatter Graph**Regression analysis**Method 2: Linear Estimation • = linest (y range, x range,1,1) • Mark 5x2 block around formula • F2 shift-control-enter Note: Can use multiple x’s with this method**Regression analysis – Elasticity of Transmission**• Calculating the elasticity of transmission from P1 to P2 • Regression analysis of P2 = a + bP1 • Regression coefficient b is ΔP2 / ΔP1 • Transmission elasticity is (ΔP2 / P2) / (ΔP1 / P1) • So transmission elasticity = b * (AVP1 / AVP2) where b = regression coefficient AVP2 = average of P2 AVP1 = average of P1**Regression analysis**• Is the relationship between prices statistically significant? • The t statistic indicates whether a relationship between two variables is statistically significant or not • The t statistic is calculated as t = b/SE where b is the coefficient and SE is the standard error of the coefficient • In general, a t statistic above 2 or below -2 is statistically significant • To get the t statistics, it is necessary to use Method 2 and calculate t • In this example t > 2, so there is a statistically significant relationship**Regression analysis – Exercise Notes**• In Worksheets 2-7, • The yellow cells (B4 – B9) define the characteristics of the random data generated, the “true” value of the parameters. • Columns B and C contain the prices generated • Graphs show the patterns in the price data • The scatter graph includes a trendline – the line best describing the relationship between the two prices • The green box shows the result of regression analysis on the price data, the estimated values of the parameters. • Each time you press F9, it will regenerate new prices, graphs, and regression results**Regression analysis – Exercise 1**• In Worksheet 2, • Change the coefficient in the yellow box (cell B8) from 1 to 3 and observe the effect on the graphs and the regression results, particularly the estimated coefficient in cell F32 • Notice that the estimated coefficient (F32) is similar to but not exactly equal to the “true” coefficient (F8) • Change the standard deviation of e (cell B9) from 10 to 40 and observe the effect on the graphs and the regression results, particularly the R2 • In Worksheet 3, • Repeat the exercises above • Notice that the estimated coefficient is less accurate (ie not as close to the true value) as in Worksheet 2**Regression analysis – Exercise 2**• In Worksheet 8 [Data], • Use regression analysis to examine the relationship between rice prices in Nampula and rice prices in Maputo • What is the coefficient? This question can be answered using either Method 1 (graph) or Method 2 (linest function) • What is the value of R2? This question can be answered using the correl function. • Is the relationship statistically significant? In order to calculate the t statistic, you will need to use Method 2 (linest function) • Note: A box has been created in sheet 8 [Data] to help with this exercise.**Non-stationarity – Definition**• What is a non-stationary variable? • A variable that does not tend to go back to a mean value over time, also called “random walk”**Non-stationarity – Problem**• Why are non-stationary variables a problem? • If prices are non-stationary, regression analysis will give misleading results • With non-stationary variables, regression analysis may indicate that there is a statistically significant relationship even when there is NO relationship**Non-stationarity – Diagnosis**• How do you identify non-stationarity? • Several tests, most common one is the Augmented Dickey-Fuller test • Cannot easily be done in Excel, but Stata and SPSS can do it easily • Price data are usually non-stationary • Of 62 African staple food prices tested, most (60%) were non-stationary**Non-stationarity – Solution**• How do you analyze non-stationary prices? • Simple approach (with Excel) • First differences (ΔP = Pt – Pt-1) are usually stationary • Regress ΔP1 on ΔP2, possibly with lags • Co-integration analysis (with Stata) • Test to see if prices are co-integrated, meaning that P2-b*P1-a is stationary • If prices are co-integrated, run error correction model (ECM) • ECM gives estimates of • Long-run transmission • Short-run transmission • Speed of adjustment to long-run equilibrium**Non-stationarity – Exercise 1**• Use Worksheet 4, which generates stationary data with no relationship between P1 and P2 • Notice that the t statistic is small, indicating (correctly) that there is no relationship between P1 and P2 • Use Worksheet 5, which generates non-stationary data with no relationship between P1 and P2 • Notice that, although the graph shows that there is no relationship between P1 and P2, the t statistic is large, indicating (incorrectly) that there is a relationship**Non-stationarity – Exercise 2**• Use Worksheet 6, which generates non-stationary data with no relationship between P1 and P2 • Calculate ΔP1 and ΔP2 in columns D and E • In D15, type =B15-B14 • Copy and paste this equation to D15:E513 (cells in yellow) • The worksheet will automatically generate two graphs, correlation coefficient, and regression results • Verify that graphs of ΔP1 and ΔP2 correctly show no relationship between them • Verify that t statistic is high in spite of the fact that the prices are not related, confirming that regression results are misleading when data is non-stationary.**Non-stationarity – Exercise 3**• Use Worksheet 7, which generates non-stationary data with a relationship between P1 and P2 • Calculate ΔP1 and ΔP2 in columns D and E • In D15, type =B15-B14 • Copy this equation to D15:E513 • Worksheet will fill in the two blank graphs, correlation coefficient, and regression results • Verify that graphs of ΔP1 and ΔP2 correctly show a relationship between them • Verify that the R2 is relatively high • Verify that t statistic is high, correctly indicating a relationship between ΔP2 and ΔP1**Conclusions**• Price transmission occurs between markets, between stages of a market channel, and between commodities… but not always • Correlation coefficient is easy to calculate and interpret but gives limited info • Regression analysis • Can be done in Excel but easier in Stata • Gives estimate of price transmission • Can take into account lagged effects • But is misleading if prices are non-stationary**Conclusions**• Non-stationarity • Means prices follow a “random walk” • Can be tested with Stata • If prices are non-stationary, need to • At minimum, regress first-differences (can be done in Excel) • Preferably, carry out co-integration analysis (requires Stata)**References (1)**• Conforti, P. 2004. Price Transmission in Selected Agricultural Markets. FAO Commodity and Trade Policy Research Working Paper No. 7. Rome. http://www.fao.org/docrep/007/j2730e/j2730e00.htm#Contents • Dawe, D. (2008) Have Recent Increases in International Cereal Prices Been Transmitted to Domestic Economies? The experience in seven large Asian countries. ESA Working paper. Rome: FAO. • Keats, S., S. Wiggins, J. Compton, and M. Vigneri. 2010. Food price transmission: Rising international cereals prices and domestic markets. London: ODI. http://www.odi.org.uk/resources/download/5079.pdf**References (2)**• Minot, N. 2010. “Transmission of world food price changes to markets in sub-Saharan Africa.” Discussion Paper No. 1059. International Food Policy Research Institute, Washington, DC. http://www.ifpri.org/publication/transmission-world-food-price-changes-markets-sub-saharan-africa • Rashid, S. 2004. Spatial integration of maize markets in post-liberalized Uganda. Journal of African Economies, 13(1), 103-133. • Vavra, P. and B. K. Goodwin (2005), “Analysis of Price Transmission Along the Food Chain”, OECD Food, Agriculture and Fisheries Working Papers, No. 3, OECD. http://www.oecd-ilibrary.org/docserver/download/fulltext/5lgjlnpcnrvh.pdf?expires=1300181573&id=0000&accname=guest&checksum=E74FDB4F6B64923819186AA5E7EF54E5